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94 lines
3.2 KiB
Text
94 lines
3.2 KiB
Text
-- M001: Thermodynamic Stress Kernel Module
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-- Source: burgers_heat_diffusion (3-Mathematical-Models)
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-- Kernel Function: ThermalZoneManager
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--
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-- Models CPU/memory thermal zones as 1D Burgers equation states.
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-- Thermal stress = velocity field u(x,t) where x=zone index, t=time.
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-- Viscosity ν = thermal conductivity, shock waves = hot spots.
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-- Truth Seal: [ SSS-ENE-THERMAL-2026-05-03 ]
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module M001_ThermodynamicStress where
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import BaseTypes
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import Semantics.Q16_16 (Q16_16, add, sub, mul, div, ofNat, zero)
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structure ThermalZone where
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id : ZoneID
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position : Q16_16 -- Spatial coordinate in thermal manifold
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temperature : Q16_16 -- Current temperature (u)
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conductivity : Q16_16 -- Thermal conductivity (ν)
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capacity : Q16_16 -- Heat capacity
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powerDissipation : Q16_16 -- Power input (forcing term)
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neighbors : Array ZoneID -- Adjacent zones (for Laplacian)
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def initThermalState (zones : Array ThermalZone) : ThermalState :=
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{ zones := zones
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, dt := Q16_16.ofNat 1 -- 1 second timestep
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, dx := Q16_16.ofNat 1 -- 1 zone spacing
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, t := Q16_16.zero
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}
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-- Burgers RHS: du/dt = ν·d²u/dx² - u·du/dx + forcing
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-- Discretized with central differences
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def burgersRHS (state : ThermalState) (idx : Nat) : Q16_16 :=
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let zone := state.zones[idx]
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let ν := zone.conductivity
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let u := zone.temperature
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-- Laplacian d²u/dx² = (u[i-1] - 2u[i] + u[i+1]) / dx²
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let left := state.zones[idx-1].temperature
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let right := state.zones[idx+1].temperature
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let laplacian := div (sub (add left right) (mul (Q16_16.ofNat 2) u)) (mul state.dx state.dx)
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-- Advection u·du/dx = u·(u[i+1] - u[i-1]) / 2dx
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let advection := mul u (div (sub right left) (mul (Q16_16.ofNat 2) state.dx))
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-- Forcing = power dissipation / capacity
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let forcing := div zone.powerDissipation zone.capacity
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-- RHS = ν·laplacian - advection + forcing
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add (sub (mul ν laplacian) advection) forcing
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def thermalStep (state : ThermalState) : ThermalState :=
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let newZones := state.zones.map (\zone idx =>
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let rhs := burgersRHS state idx
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{ zone with temperature := add zone.temperature (mul rhs state.dt) }
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)
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{ state with zones := newZones, t := add state.t state.dt }
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-- Stress metric: max |du/dx| (thermal gradient shock indicator)
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def thermalStressMetric (state : ThermalState) : Q16_16 :=
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let gradients := state.zones.map (\zone idx =>
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if idx < state.zones.size - 1 then
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let right := state.zones[idx+1].temperature
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abs (sub right zone.temperature)
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else
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Q16_16.zero
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)
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gradients.maximum
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-- Kernel syscall interface: get thermal stress recommendation
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def syscallThermalStress (zoneId : ZoneID) : IO ThermalReport := do
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let zone ← findZone zoneId
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let state ← readThermalState
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let stress := thermalStressMetric state
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let recommendation :=
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if stress > THERMAL_CRITICAL then
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.EmergencyThrottle
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else if stress > THERMAL_WARNING then
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.ReduceClock
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else
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.Normal
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return {
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zone := zone
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temperature := zone.temperature
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stressLevel := stress
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action := recommendation
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timestamp := now ()
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}
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end M001_ThermodynamicStress
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